Updated

Get ready for the rematch.

Alaska Sen. Lisa Murkowski, who lost in a stunning upset to Tea Party-backed Joe Miller in the Republican Senate primary last month, announced her plan Friday to mount a write-in candidacy for the general election in November.

Her announcement came at a late afternoon rally in Anchorage as supporters surrounded her and chanted: "Run, Lisa, Run!"

Murkowski acknowledged she made mistakes during the primary campaign, but promised she'll be more aggressive this time in running against Miller.

"The gloves are off," she said.

Murkowski was swayed by a recent poll showing that if she ran as an independent, she'd beat Miller by 6 percentage points and Democratic candidate Scott McAdams by 18 percentage points, said Andrew Halcro, a former Republican candidate for governor.

But the write-in campaign will be an uphill battle for Murkowski because her name won't appear on the ballot and she won't have the support of the Republican establishment. Republican political action committees have already begun giving to Miller, who won the nomination after waiting nearly two weeks for state election officials to count the absentee ballots that guaranteed the win.

Murkowski, though, has $1.4 million in the bank to spend on her independent bid, and she will be the only seasoned politician in the race.

Former Alaska Gov. Sarah Palin urged Murkowski on Twitter Friday afternoon to recognize that the state's primary voters demonstrated their support for Miller, a tea party favorite.

"Listen to the people, respect their will," said Palin, the 2008 Republican vice presidential nominee. "Voters chose Joe instead."

The Democratic Senatorial Campaign Committee instantly expressed delight in Murkowski's decision.

"Lisa Murkowski's decision to mount a write-in campaign is just the latest example of the Republican Party cannibalizing itself," DSCC spokeswoman Deirdre Murphy said in a statement. "From the tip of Florida, to the beaches in Delaware, all the way to the island off Alaska, the Republican Party heads into November with deep and serious divisions."

Murphy was referring to Gov. Charlie Crist's decision to ditch the Republican Party and run as an independent in the Florida Senate race after trailing badly to conservative Marco Rubio and Christine O'Donnell's upset victory over veteran Rep. Mike Castle in the Delaware GOP primary on Tuesday.

"Alaska voters now have three options in November: a Washington insider who supports the failed economic policies of the past, an extremist who wants to end Social Security and Medicare, and a small-town mayor would put Alaskan families first," Murphy added.

During the Alaska primary, the Tea Party Express ran ads supporting Miller and distorting Murkowski's position on the new health care law. She called the California-based organization an "outside extremist group."

The Associated Press and Fox News' Dan Springer contributed to this report.